connecting mathematical knowledge and...

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The research reported here was supported by the National Science Foundation, through a grant to the University of Michigan. The opinions, findings, and recommendations expressed are those of the authors and do not represent views of the National Science Foundation.

CONNECTING MATHEMATICAL KNOWLEDGE AND DISPOSITIONS

WITH PEDAGOGICAL SKILLS

Meghan Shaughnessy & Timothy BoerstNCTM Research Conference • San Diego, CA • April 2, 2019

Acknowledging our colleagues on this study: Merrie Blunk, Rosalie DeFino, Erin Pfaff, Xueying Ji Prawat, & Emily Theriault-Kimmey

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creativecommons.org/licenses/by-nc-nd/4.0/

© 2019 Mathematics Teaching and Learning to Teach • University of Michigan School of Education • 48109 • [email protected]


OUR GOAL FOR MATHEMATICS TEACHER EDUCATION: WELL-STARTED BEGINNERS

Preparing elementary teachers of mathematics who are ready for responsible professional work with students from the day they assume responsibility for classrooms of their own through learning experiences that integrate and advance:§ Mathematical Knowledge for Teaching (MKT)§ Productive mathematical dispositions § Skill with essential teaching practices

… all with room (and tools!) for further growth and development

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ZOOMING IN ON OUR STUDY

The field acknowledges that mathematical knowledge and mathematical dispositions impact teaching, but how and in what way?

How are teachers’ eliciting and/or interpreting of a student thinking impacted by their mathematical knowledge and/or dispositions?

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STUDY DESIGN

§ Participants: 24 preservice teachers, range of points in the teacher education program

§ Data Collection Part 1:§ Measure of knowledge of four specific subtraction approaches§ Measure of disposition towards four subtraction approaches

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AN EXAMPLE: STUDENT APPROACHES TO SUBTRACTIONShowing mathematical knowledge though:§ Describing the steps of the

process and their sequence§ Justifying and generalizing§ Applying the approach to

another problem

Showing mathematical dispositions toward the process through responses to questions:§ Is the approach sensible?§ Would you use the process yourself?

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STUDYING THE CONNECTION OF MKT, DISPOSITION, AND TEACHING PRACTICESimulations are approximations of practice that can be used to study the connections among MKT, disposition, and teaching practice.Simulations:§ are commonly used in many professional fields§ place authentic, practice-based demands on a participant § purposefully suspend or standardize some elements of the

practice-based situation § can provide insights that are not possible or practical to

determine in real-life professional contexts

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STUDY DESIGN

§ Participants: 24 preservice teachers, range of points in the teacher education program

§ Data Collection Part 1:§ Measure of knowledge of four specific subtraction approaches§ Measure of disposition towards four subtraction approaches

§ Data Collection Part 2:§ Three simulation assessments, including:

§ one that was high preference/high mathematical knowledge § one that was low preference/low mathematical knowledge§ one that was low preference/high mathematical knowledge

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Strong math knowledge & Positive disposition

Weak math knowledge & Negative disposition

Strong math knowledge & Negative disposition

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Stronger Mathematical Knowledge

Weaker Mathematical Knowledge

Negative Disposition

PositiveDisposition




STRUCTURE OF THE TEACHING SIMULATION

The preservice teacher1. Prepares for an interaction with a standardized student

about one piece of student work2. Interacts with the “student” to elicit the student’s thinking 3. Interprets the student’s thinking in a follow up interview,

using evidence from the interaction

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FINDINGS

00.10.20.30.40.50.60.70.80.9

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Eliciting thestudent's proces

Eliciting thestudent's

understanding

Interpreting thestudent'sprocess

Interpreting thestudent's

undestanding(open ended)

Interpreting thestudent's

understanding(predetermined)

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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge & Negative disposition

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Eliciting the student’s understanding was stronger in a strong math knowledge/positive disposition situation compared to a weak math knowledge/negative disposition situation

ELICITING OF THE STUDENT’S UNDERSTANDING

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0

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p < .001




Does mathematics knowledge matter when disposition is about the same?Eliciting the student’s understanding was stronger when math knowledge was strong compared to a weak math knowledge situation


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0

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p = .032




Does disposition matter when math knowledge is about the same? Eliciting the student’s understanding was stronger in a positive disposition situation compared to a negative disposition situation (marginally significant)


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0

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p = .059




Stronger knowledge of the mathematics of the algorithm and having a positive disposition towards the algorithm (relative to other algorithms) both had a positive impact on eliciting the student’s understanding.

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p < .001 p = .059p = .032


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Stronger knowledge of the mathematics of the algorithm and having a positive disposition towards the algorithm (relative to other algorithms) both had a positive impact on eliciting the student’s understanding.

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p < .001 p = .059p = .032Why? Mathematical knowledge of the

algorithm may support PSTs in identifying understandings to ask about (and in posing a question focused on that understanding)

Why? Positive disposition towards the algorithm may result in PSTs knowing

that the algorithm is understandable and that there are questions to ask about it


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INTERPRETING THE STUDENT’SUNDERSTANDING (OPEN ENDED)Interpreting the student’s understanding was stronger in a strong math knowledge/positive disposition situation compared to a weak math knowledge/negative disposition situation

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0

0.2

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0.6

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1

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Strong math knowledge & Positive dispositionWeak math knowledge & Negative dispositionStrong math knowledge and Negative disposition

p = .002




INTERPRETING THE STUDENT’S UNDERSTANDING (OPEN ENDED)Does mathematics knowledge matter when disposition is about the same?Interpreting the student’s understanding was stronger when math knowledge was strong compared to a weak math knowledge situation

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0

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p < .001




INTERPRETING THE STUDENT’S UNDERSTANDING (OPEN ENDED)Does disposition matter when math knowledge is about the same? Disposition did not appear to impact interpreting the student’s understanding

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0

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No significant difference




INTERPRETING THE STUDENT’S UNDERSTANDING (OPEN ENDED)Stronger knowledge of the mathematics of the algorithm relative to other algorithms had a positive impact on interpreting the student’s understanding. Disposition did not appear to impact.

0

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p = .002 p < .001 No significant difference

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INTERPRETING THE STUDENT’S UNDERSTANDING (OPEN ENDED)Stronger knowledge of the mathematics of the algorithm relative to other algorithms had a positive impact on interpreting the student’s understanding. Disposition did not appear to impact.

0

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p = .002 p < .001 No significant difference

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Why? Mathematical knowledge of the algorithm may support PSTs in identifying understandings to make inferences about and in making sense of evidence gathered




INTERPRETING THE STUDENT’S UNDERSTANDING (PREDETERMINED)

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p = .016 No significant difference p = .030

Positive disposition towards the algorithm relative to other algorithms had a positive impact on interpreting the student’s understanding of a specific idea. Mathematical knowledge did not appear to impact.

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INTERPRETING THE STUDENT’S UNDERSTANDING (PREDETERMINED)

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p = .016 No significant difference p = .030

Positive disposition towards the algorithm relative to other algorithms had a positive impact on interpreting the student’s understanding of a specific idea. Mathematical knowledge did not appear to impact.

0

0.2

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Why? Positive disposition towards the algorithm may support PSTs in trusting/not discounting the

understandings conveyed about the approach




QUESTIONS FOR CONSIDERATION

§ What are some possible explanations for the findings… § Eliciting and interpreting process: not markedly impacted by

differences in knowledge or disposition.§ Eliciting understanding: impacted by differences in knowledge

and disposition.§ Interpreting understanding (open ended): impacted by

differences in knowledge, but not disposition§ Interpreting understanding (predetermined): impacted by

differences in disposition, but not knowledge

§ What are some implications of these findings for TE?

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QUESTIONS? WANT MORE INFORMATION?http://sites.soe.umich.edu/at-practice/



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